The realization space is
  [1   0   1   1   x1 - 1              x1^2   0   x1 - 1    0       x1 - 1    1]
  [0   1   1   1     x1^2   2*x1^2 - x1 + 1   0        0   x1         x1^2   x1]
  [0   0   0   1     x1^2              x1^2   1      -x2   x2   x1*x2 - x2   x2]
in the multivariate polynomial ring in 2 variables over ZZ
within the vanishing set of the ideal
Ideal with 2 generators
avoiding the zero loci of the polynomials
RingElem[x1, x2, x2 - 1, x1^2 - x1*x2 + x2, x1 - x2, x1^3 - 2*x1^2*x2 + x1*x2 - x2, x1^3 - x1^2*x2 - x1^2 + x1*x2 - x2, x1 - 1, x1^3 - 2*x1^2 + x1 - 1, x1^2 - x1 + 1, x1^2 - x1 + x2, x1^4 - x1^3*x2 - x1^3 + 3*x1^2*x2 - 2*x1*x2 + x2, x1^4 - 2*x1^3*x2 + 3*x1^2*x2 - 2*x1*x2 + x2, x1^3 - x1^2*x2 + x1*x2 - x2, 2*x1^2 - x1 + 1, x1 + x2 - 1, x1^2 + x2]